Question: Solve for $x$ : $x^2 + 19x + 90 = 0$
Answer: The coefficient on the $x$ term is $19$ and the constant term is $90$ , so we need to find two numbers that add up to $19$ and multiply to $90$ The two numbers $9$ and $10$ satisfy both conditions: $ {9} + {10} = {19} $ $ {9} \times {10} = {90} $ $(x + {9}) (x + {10}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 9) (x + 10) = 0$ $x + 9 = 0$ or $x + 10 = 0$ Thus, $x = -9$ and $x = -10$ are the solutions.